Research: actual Turyn profiles have asymmetric block rank 9d (no new kappa)

[yonghaozheng64-commits]

For every characteristic-two field and every positive integer block size d, each complete canonical 7,680-port Turyn profile has minimum asymmetric block-fitting rank exactly 9d, with diagonal blocks I_d and zero blocks on actual active edges.

This contribution consistently lifts PR598's per-profile parity-clique restrictions to twenty actual ports in each profile, then independently verifies the upper fit on every complete profile. DominikScholz / PR598, incorporated head 615ca6f, deserves credit for the general parity-projector argument, the predecessor geometry, and the nine-dimensional upper map. The new part is the consistent actual-port lift and independent full-profile reconstruction. PR898 accelerates a historical affine Leech-minor audit; it supplies neither this lift nor the asymmetric-block result, and none of its code is reused. The exact comparison and pinned primary sources are in research/turyn-profile-parity-lift/COMPARISON.md.

Scope: this is a per-profile result. It does not establish unrestricted global rank 27, exclude arbitrary global 25-dimensional fittings, improve kappa, supply a multiplication supplier, or constitute a formal verification of the full multiplication theorem. The ordinary degree-three polynomial-calculus appendix independently corroborates the different earlier 24-port symmetric obstruction over all characteristic-two fields; its 57-variable-edge core is inclusion-minimal with fixed anchors, not globally edge-minimum.

Draft integration limitation: the original validation base is 91a2094. Its preserved baseline deliberately pins the historical PR799 selected record. This branch applies the identical 44 added files on main 2921874, whose selected record is different. The baseline checker on this branch fails with "Source pin mismatch: certificates/selected-result.json". Context adaptation is outstanding; this PR is not presented as merge-ready. No selected record, source pin, frozen baseline, upstream source, or unrelated file has been overwritten or relaxed. Integration needs an immutable historical checkpoint/adapter, review of changed dependency pins, and a focused rerun.

Validation evidence:

• The supplied original-base receipts record four checkers and all 40 test groups in both normal and optimized modes, fresh-base patch application, byte-identical producer replay, corruption controls, and minimal offline relocation.
• Publication preparation independently checked all 99 archive manifest entries, the exact patch hash, all 12 consumed historical Git source blobs, and clean historical-index patch application with exactly 44 additions.
• Native Windows reruns are not a complete passing validation: the four checkers and the 33 focused unit-test groups passed in both modes against the frozen offline inputs, with targeted retries required for optimized full-profile checks. The seven-group offline package suite did not pass: rebuild byte comparisons differ because of CRLF serialization, and some reruns encountered intermittent native process failures / TypeErrors. These observations do not replace the supplied original-base receipts.
• The full-profile verifier exhausts all 29,487,360 unordered pairs per profile via its complete root-fiber partition; there is no edge sampling.
• No repository-wide make verify, selected-supplier cold replay, Lean build, hosted CI success, or independent human review is claimed.

To reproduce the original-base validation, apply this PR's two-directory diff to the exact original base (rather than rewriting newer main's selected record), then run Python 3.10+ with its standard library only:

for flags in "-I -B" "-I -O -B"; do
  for script in \
    research/turyn-profile-cnf/verify.py \
    research/turyn-profile-parity-lift/verify.py \
    research/turyn-profile-parity-lift/verify_full_profiles.py \
    research/turyn-profile-parity-lift/algebraic/verify.py \
    research/turyn-profile-cnf/test_verify.py \
    research/turyn-profile-parity-lift/test_verify.py \
    research/turyn-profile-parity-lift/test_full_profiles.py \
    research/turyn-profile-parity-lift/algebraic/test_verify.py \
    research/turyn-profile-parity-lift/test_package.py
  do
    python3 $flags "$script" || exit 1
  done
done

Only research/turyn-profile-cnf/ (15 files) and research/turyn-profile-parity-lift/ (29 files) are added. The archive, fetched context, publication logs, and other project files are excluded. Substantial AI assistance was used for the research, implementation, verification, and preparation of this submission. Predecessor attribution and Apache-2.0 notices are retained.